L REVISED AND ENLARGED EDITION. 



SHORT METHODS 



COMPUTING 



Interest m» Discount. 



•w- 



^~ 



100 Days Interest Method. | 



Simple Interest, Bank Discount, Compound Interest. 



BY 



V 
[EKKY <50IiDM£N, 



Author of the Arithmetical Detector.' 



100 Days Average Method," "Combination Discount Calculator" Etc. (< 

(C 

C 



CHICAGO, 135 



COPYRIGHT, 1SS4, BY HENRY GOLDMAN. 
ALL RIGHTS RESERVED. 



REVISED AND ENLARGED EDITION. 



SHORT METHODS 

FOR 

COMPUTING 



Interest snd Discount. 



loo Days Interest (Dethod. 

Simple Interest, Bank Discount, Compound Interest. 

BY 

HEHKY '(SOLDMSH, 

Author of the 'arithmetical Detector.' 
"100 Days Average Method," "Combination Discount Calculator" Etc. 

" 



Chicago, ia^e. NOV ] a) 

X^f* WASHtft<*- 



COPYRIGHT, 1884, BY HENRY GOLDMAN. 
ALL RIGHTS RESERVED. 



fit** 



LC Control Number 




tmp96 027242 



PREFACE. 

Accuracy and speed in computing interest and discount are 
important accomplishments; that they are so rarely found proves 
to a great extent the deficiency of the methods hitherto intro- 
duced. 

The author offers in the following pages a method, pronounced 
by experts as the shortest and simplest interest method known, 
and which, according to his own judgment, leaves nothing to be 
desired. It can be easily acquired and when once learned is 
hardly ever to be forgotten. Being applicable to all cases that 
may possibly arise, it is bound to win its way into general use. 

For Hank Discount no more satisfactory method has ever been 
invented. Based on a strictly scientific principle, it combines 
all the advantages of the so-called Table methods, without 
sharing any of their faults. The time required for opening the 
table and looking for page etc., is more than sufficient to as- 
certain the result by this new method, saving time and inconven- 
ience. As another advantage the author claims that errors re- 
sulting from the neglect of fractions, which in the aggregate of 
many items may cause a considerable difference, are practically 
avoided by the reduction of the high rate of 36% to any given 
ate, decreasing all differences from three to twelve times. The 
consideration of the tens of the cents of the principal, when- 
ever the number of days exceeds 100, is another of the many 
good features of this method, while the thorough application of 
the decimal principle places it at the head of all methods pre- 
viously taught. 

This pamphlet contains also a simplified rule for ascertaining 
the present value of a note, an improved method for compound 
interest, etc. 

A fair tiial of the methods herein given will convince even 
the most skeptical of their excellence. 

THE AUTHOR. 



Is a compensation for the use of money; Prinxi- 
pal, the money on which Interest is computed; 
Rate, the number of per cent., and Amount, the 
sum of Principal and Interest. 

1DD HAYS INTEREST METHDH. 

To obtain the interest for ioo days, 10 days, or 
I day, divide the principal by one of the divisors of 
the following table, according to the Rate, and 
add or deduct, if necessary, the part which the 
corresponding column indicates. 

The divisors for the most frequent rates can be remembered 
without difficulty, being the result of 36 divided by the given 
rate. The division of the principal is carried out to the tens 
of the cent ; two places of the result are pointed off as cents, 
the remaining figures represent dollars of interest for 100 days. 

The interest for any desired number of days 
can be easily found by multiplying the hundreds, 
tens, or units of days by the corresponding amount 
of interest and adding these products together. 

If the number of days is between 90 and 100, deduct from 
the interest for 100 days as many times the interest for 1 day 
as there as there are days less. The interest for 9 days equals 
the interest for 10 days less the interest for one day. 25 days 
interest is one quarter of a hundred days interest, etc. 



— 5— 
TABLE. 



RAT] 


DIVISORS. 


PARTS. 


Per cent. 


Divide by 


To be added. 


To be deducted. 


1 


oG 






.: 


18 

12 








12 


One sixth. 




4 


9 








8 








6 




sixth. 




6 




One-twelfth. 


6 


6 








G 


One-twelfth. 






G 


One-sixth. 






6 


One-quarter. 






6 


One-third 






4 




One-eighteenth. 


9 


4 








4 


One eighteenth. 




in 


3 




One-sixth. 


11 


3 




One twelfth. 


12 


3 







EXAMPLES. 
$763-— at 6 % for 93 days ? 

6)763.0 



1271 

0-127X7= 89 



^Interest at 69^ for 100 days. 

a a a -r ( i 

Answer, $11 -82 ^Interest at 6% for 93 days, 
$136-43 — at 8$ for 112 days? 

6(136-4(3 

2*27 ^Interest at 6% for 100 days. 
-X 76;= " _Hc_ " <: 



53 03=Tnterest at 8$ for 100 days. 

0-303X1=. 3°= " " I0 " 

0-030X2= 6= " " 2 " 

Answer, $3-39— Interest at 8% for 112 days. 

If the time is given in months, reduce first to 
days, figuring the month at 30, or at the exact 
number of days. Interest for years should be 
computed separately by multiplying the principal 
by the product of the rate and number of years, 



-6 — 

BANK DISCOUNT. 

Any principal showing its own interest at 36% 
for 100 days, 10 days, or 1 day by removing the dec- 
imal point 1, 2 or 3 places to the left, the interest 
for any given number of days at 36% can be easily 
found by multiplying the interest on each note for 
1, 10 or 100 days by the units, tens or hundreds of 
the corresponding number of days. These pro- 
ducts, added together form the Interest or Bank 
Discount on all notes at 36%. 

To obtain the interest at any given rate, divide 
the sum of the products by one of the divisors of 
the table (page 5), according to the rate, and add 
or deduct the part which the corresponding column 
indicates. 

Note. The dollars of any principal show the interest in 
cents for 10 days at 36$,. Ten times the interest for 10 days 
represent the interest for 100 days, and one-tenth of it the inter- 
est for I day. 

In computing interest the fractions of cents must be taken in 
consideration. For instance: he interest on $345.63 at 36$, 

For 100 days is $34.56, 10 days $3.46, 1 day 35c. 
EXAMPLE. 

Bank Discount on the following notes at *]c/ ? 

$360.00 for 16 days f 3.60 



72.18 " 29 " f 1-44 



2.16 
44 
65 



129.36 * 34 * ......... (3 88 



•52 

87.50 ■ 80 " 7-o° 

N [4-03 

4029 •' 112 (< -j -4° 



6)2 3.76 

Interest at 6 % 3-9 6 

" «±jk + £ - 66 

Answer: In'erest at 7 % $4.62 



— 7— 

PRESENT WDRTH, 

To ascertain the Principal which at a given rate and in a giv- 
en number of days, produces a given amount. 

Multiply one-sixth of the rate by one-sixth of 
the number of days, remove the decimal point three 
places to the left, add one unit to the product, and 
divide the given amount by this sum. 

EXAMPLE. 
Present Worth of $1000, due in 93 days, Rate 6% ? 
6)93 6)6(1 

1,015*5)1000 00(98473, Answer. 
86050 
48100 
74800 
37150 
To ascertain the Amount which after deducting the Interest or 
bank discount at a given rate and for a given number of da/s r 
/eaves a given principal. 

Apply the rule stated above, with the deviation 
that instead of adding one unit to the product, 
subtract the product from one unit, and substitute 
for the unknown amount the given principal. 

CDMFDUND INTEREST 

is the interest on the sum of a given principal and 
its interest, added in certain intervals, either annu- 
ally or semi-annually. 

The compound interest of $1.00 from one to ten 
years can be obtained by multiplying successively 
the rate, squared rate, cubed rate, etc., by the fac- 
tors of the following table, according to the num- 
ber of years, placing each following product two 
places to the right under the one preceding, and 
rinding their total. 



• 


COMPOUND INTEREST FACTORS. 




3Q 


© 


3 


o 


© 


© 


© 


© 


© 


~ 


C: 


_ 


-+J 


q 


o 


© 


© 


s 


© 


© 


© 




l w 


c3 


X 


© 


© 


o 


© 


© 


© 




— > 


>H 


« 


X 


© 
© 


© 


© 

© 


3 
© 


© 


© 

© 


^ 






— 
c5 


© 
X 




















1 


1 


M 


© 


© 


© 

© 


© 
© 


© 
© 


2 


© 
© 








83 


© 


X 


© 
X 


© 
© 

© 


© 


© 
© 

© 




2 


2 


1 


1 










o3 


CO 

-1-3 

1 


% 


X 

© 

m 


© 

X 

00 ( 

© 

i 
i 


3 
© 
© 

X 

o 
13 

— 

08 


— 


g 

a 


3 


3 


1 


5 


4 


4 


6 


4 


1 


X 


5 


5 


10 


10 


5 




6 


6 , 


15 


20 


15 


6 


1 




7 


7 


21 


35 


35 


21 


7 


i 




8 


8 


28 


56 


70 


56 


28 


8 


C3 
33 


9 


9 


36 


84 


126 


126 


84 


36 


9 


1 


M 


10 


10 


45 


120 


210 


252 


210 


120 


45 


10 


1 



Note. — These factors can be easily retained, being the mem- 
bers of progressions which stand in obvious relations to each 
other. 

EXAMPLE. 

Compound Interest on $1, for 4 years at 5$ ? 
5X4=20. . 
25X6= 150. . 
125X4= 500- • 
625X1= 625 

!fo-2i 550625= Answer. 

It is'sufficient for all practical purposes to go 
only as far as the 3rd power of the rate. 



— 9— 
i tain the compound interest on any given 
principal, multiply the same by the compound in- 

5t Of Sl.OO. 

• inpound interest can also be computed semi- 
annually which is equivalent to the annual compound 
interest for twice the number of years at half the 

To find, approximately, tli£ number of years in 
which any principal doubles itself by the accumu- 
lated compound interest, divide 72 by the given 
rate. 

ANNUITIES, 

To find the annuity with which to pay Si in a 
given number of years, divide the rate by the com- 
pound interest, add the rate to the quotient, and 
remove the decimal point two places to the left. 

EXAMPLE. 

Annuity to nay $1 in 4 years, at 5$ ? 
Compound Interest, 0-2155) 5000 ( 23-20 

6900 5 

m 435° •282o==Annuity. 

40 

To find the amount to which an annual invest- 
ment of Si will accumulate, divide the compound 
interest at the given rate and for the given number 
of years by the rate, and remove the decimal point 
two places to the right. 

EXAMPLE. 
$1 annual investment for 4 years at 5 

5)0-2155, Compound Interest. 
$4*31, Accumulated Amount. 

The results obtained for $\ can be applied to 
any amount by simple multiplication. 



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"ioo Days Average Method." 

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"The Expert Calculator." 

Collection of Rules and Methods for Rapid Figuring. 
Practical hints to Book-keepers and Accountants. 

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A rapid method for deducting discounts. 

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My printed publications, containing the systems, methods 
and rules mentioned, will be sent to any direction postpaid on 
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All orders, inquiries or communications intended for the 
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HENRY GOLDMAN, 

116 LASALLE ST., ROOM 6, 

CHICAGO, ILL. 




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